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Global sensitivity analysis for multivariate outputs based on multiple response Gaussian process model

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  • Liu, Fuchao
  • Wei, Pengfei
  • Tang, Chenghu
  • Wang, Pan
  • Yue, Zhufeng

Abstract

The computational models in real-world applications commonly have multivariate dependent outputs of interest, and developing global sensitivity analysis techniques, so as to measure the effect of each input variable on each output as well as their dependence structure, has become a critical task. In this paper, a new moment-independent sensitivity index is firstly developed for quantifying the effect of each input variable on the dependence structure of model outputs. Then, the multiple response Gaussian process (MRGP) surrogate model with separable covariance is introduced for efficiently estimating the existing sensitivity indices for multiple response models and the newly developed one. Some indices are analytically derived based on the hyper-parameters of the MRGP model, while others are numerically estimated. One numerical example and three engineering examples are introduced to compare the newly developed sensitivity index with the classical ones, and to demonstrate the effectiveness of the MRGP-based method in estimating these sensitivity indices.

Suggested Citation

  • Liu, Fuchao & Wei, Pengfei & Tang, Chenghu & Wang, Pan & Yue, Zhufeng, 2019. "Global sensitivity analysis for multivariate outputs based on multiple response Gaussian process model," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 287-298.
    • Handle: RePEc:eee:reensy:v:189:y:2019:i:c:p:287-298
    DOI: 10.1016/j.ress.2019.04.039
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    References listed on IDEAS

    as
    1. Wang, Pan & Lu, Zhenzhou & Zhang, Kaichao & Xiao, Sinan & Yue, Zhufeng, 2018. "Copula-based decomposition approach for the derivative-based sensitivity of variance contributions with dependent variables," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 437-450.
    2. Borgonovo, E., 2007. "A new uncertainty importance measure," Reliability Engineering and System Safety, Elsevier, vol. 92(6), pages 771-784.
    3. Wei, Pengfei & Lu, Zhenzhou & Song, Jingwen, 2015. "Variable importance analysis: A comprehensive review," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 399-432.
    4. Li, Heping & Deloux, Estelle & Dieulle, Laurence, 2016. "A condition-based maintenance policy for multi-component systems with Lévy copulas dependence," Reliability Engineering and System Safety, Elsevier, vol. 149(C), pages 44-55.
    5. S. Conti & J. P. Gosling & J. E. Oakley & A. O'Hagan, 2009. "Gaussian process emulation of dynamic computer codes," Biometrika, Biometrika Trust, vol. 96(3), pages 663-676.
    6. Garcia-Cabrejo, Oscar & Valocchi, Albert, 2014. "Global Sensitivity Analysis for multivariate output using Polynomial Chaos Expansion," Reliability Engineering and System Safety, Elsevier, vol. 126(C), pages 25-36.
    7. Li, Dian-Qing & Tang, Xiao-Song & Phoon, Kok-Kwang, 2015. "Bootstrap method for characterizing the effect of uncertainty in shear strength parameters on slope reliability," Reliability Engineering and System Safety, Elsevier, vol. 140(C), pages 99-106.
    8. E. Borgonovo & S. Tarantola & E. Plischke & M. D. Morris, 2014. "Transformations and invariance in the sensitivity analysis of computer experiments," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(5), pages 925-947, November.
    9. Emanuele Borgonovo & William Castaings & Stefano Tarantola, 2011. "Moment Independent Importance Measures: New Results and Analytical Test Cases," Risk Analysis, John Wiley & Sons, vol. 31(3), pages 404-428, March.
    10. Zhang, Yi & Gomes, António Topa & Beer, Michael & Neumann, Ingo & Nackenhorst, Udo & Kim, Chul-Woo, 2019. "Reliability analysis with consideration of asymmetrically dependent variables: Discussion and application to geotechnical examples," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 261-277.
    11. Campbell, Katherine & McKay, Michael D. & Williams, Brian J., 2006. "Sensitivity analysis when model outputs are functions," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1468-1472.
    12. Kennedy, Marc C. & Anderson, Clive W. & Conti, Stefano & O’Hagan, Anthony, 2006. "Case studies in Gaussian process modelling of computer codes," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1301-1309.
    13. Li, Luyi & Lu, Zhenzhou & Wu, Danqing, 2016. "A new kind of sensitivity index for multivariate output," Reliability Engineering and System Safety, Elsevier, vol. 147(C), pages 123-131.
    14. Wang, Guodong & He, Zhen & Xue, Li & Cui, Qingan & Lv, Shanshan & Zhou, Panpan, 2017. "Bootstrap analysis of designed experiments for reliability improvement with a non-constant scale parameter," Reliability Engineering and System Safety, Elsevier, vol. 160(C), pages 114-121.
    15. Wei, Pengfei & Liu, Fuchao & Tang, Chenghu, 2018. "Reliability and reliability-based importance analysis of structural systems using multiple response Gaussian process model," Reliability Engineering and System Safety, Elsevier, vol. 175(C), pages 183-195.
    16. Lamboni, Matieyendou & Monod, Hervé & Makowski, David, 2011. "Multivariate sensitivity analysis to measure global contribution of input factors in dynamic models," Reliability Engineering and System Safety, Elsevier, vol. 96(4), pages 450-459.
    17. Tee, Kong Fah & Khan, Lutfor Rahman & Li, Hongshuang, 2014. "Application of subset simulation in reliability estimation of underground pipelines," Reliability Engineering and System Safety, Elsevier, vol. 130(C), pages 125-131.
    18. Kucherenko, Sergei & Feil, Balazs & Shah, Nilay & Mauntz, Wolfgang, 2011. "The identification of model effective dimensions using global sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 96(4), pages 440-449.
    19. Matieyendou Lamboni, 2018. "Global sensitivity analysis: a generalized, unbiased and optimal estimator of total-effect variance," Statistical Papers, Springer, vol. 59(1), pages 361-386, March.
    20. Plischke, Elmar & Borgonovo, Emanuele & Smith, Curtis L., 2013. "Global sensitivity measures from given data," European Journal of Operational Research, Elsevier, vol. 226(3), pages 536-550.
    21. Sobol’, I.M. & Kucherenko, S., 2009. "Derivative based global sensitivity measures and their link with global sensitivity indices," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(10), pages 3009-3017.
    22. Pengfei Wei & Zhenzhou Lu & Jingwen Song, 2014. "Moment‐Independent Sensitivity Analysis Using Copula," Risk Analysis, John Wiley & Sons, vol. 34(2), pages 210-222, February.
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    Cited by:

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    3. Torii, André Jacomel & Novotny, Antonio André, 2021. "A priori error estimates for local reliability-based sensitivity analysis with Monte Carlo Simulation," Reliability Engineering and System Safety, Elsevier, vol. 213(C).

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